Answer:
When the same resistors are connected in parallel across the same EMF source, the power dissipated will also be 30 W, just like in the series configuration.
Step-by-step explanation:
When resistors are connected in series, the total resistance adds up. However, when resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. This is known as the parallel resistor formula:
1 / R_total = 1 / R1 + 1 / R2 + 1 / R3
Let's denote the resistance of each individual resistor as R (since they are equal). If three equal resistors are connected in series and dissipate 10 W each, the total power dissipated is:
P_total_series = P1 + P2 + P3
= 10 W + 10 W + 10 W
= 30 W
Now, if the same resistors are connected in parallel, the total resistance becomes:
1 / R_total_parallel = 1 / R + 1 / R + 1 / R
= 3 / R
Solving for R_total_parallel:
R_total_parallel = R / 3
Now, the total power dissipated in a parallel circuit can be calculated using the formula:
P_total_parallel = V^2 / R_total_parallel
Where V is the voltage across the parallel combination. Since the EMF remains the same, the voltage across the parallel combination is the same as the voltage across the series combination. Let's denote this voltage as V.
P_total_parallel = V^2 / (R / 3)
= 3 * V^2 / R
We know that the total power dissipated in the series circuit was 30 W. Equating the two expressions for power:
3 * V^2 / R = 30 W
Solving for V^2:
V^2 = 30 W * R / 3
V^2 = 10 W * R
Now that we have the relation between V^2 and R, we can substitute it into the formula for power in the parallel circuit:
P_total_parallel = 3 * V^2 / R
= 3 * (10 W * R) / R
= 30 W
So, when the same resistors are connected in parallel across the same EMF source, the power dissipated will also be 30 W, just like in the series configuration.